Small n factoring

[ShoeLace]

this is my understanding of ECM.

ECM is a probabilistic algorithm.

the standard listed number of curves when run has a chance of a missed factor for the given size of 37% (its like 1/e where e=2.71828183... )

(http://www.loria.fr/~zimmerma/records/ecm/params.html)

i also had thought (but may be mistaken) that it only work if EXCATLY 1 factor is within B1 and B2. eg if there are factors 123001 and 124001 would only be found if B2 is between 123001 and 124001..
ie B1=100000,B2=200000 would fail
B1=100000,B2=123500 would succeed

but i couldnt find a reference that supports this claim.
edit: found it http://www.mersenneforum.org/showthread.php?t=194
this page goes onto say ECM (and P-1) find factors that are (B1,B2)-smooth (1 factor between b1 and b2)


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Shoe Lace